Inflatable Sphere

A proposed drag augmentation alternative is to make use of an inflatable envelope to increase the area to mass ratio at the beginning of the deorbit phase (National Research Council, 1995). Such an envelope will typically have a spherical shape similar to the Echo balloon missions.

The advantage of a sphere is that the drag area will always be the same regardless of attitude. There is thus no need to stabilize the attitude, although it is likely that the satellite will self-stabilize eventually with the balloon trailing behind the host satellite.

The envelope will be susceptible to impact (like any other drag augmentation option) but where a sail can be designed to remain intact with the help of rip-stops and reinforcements, an inflated balloon will lose pressure in such an event.

There are two realistic options to maintain a rigid sphere. The first is to rigidise the envelope after inflation. This can be achieved by making use of a metal-polymer laminate and applying pressure past the tensile yield point of the metal. This removes all the creases from it, and after the gas is vented the structure remains rigid. This process was demonstrated on the Echo II mission (Staugaitis & Kobren, 1966). It should also be possible to utilize chemical rigidisation – by using a material that will harden with exposure to UV radiation.

The other alternative is to maintain a constant pressure inside the envelope so that even if it is punctured it will retain its shape (Nock, et al., 2010). In the first case, the membrane will be thicker and heavier, but in the second case the inflation system will be more complex and should be capable of sustaining pressure over an extended period.

Theory

The inflatable sphere is also a drag augmentation method, and the same theory as for a sail applies. However the aerodynamic and solar force due to an inflatable sphere will be different from that of a sail because of the different shape.

It is assumed that the sphere will be significantly larger than the host satellite, so that only the inflatable balloon surface is taken into account when modelling the aerodynamic and solar disturbances. The symmetric nature of the sphere implies that the aerodynamic and solar forces on the surface will be independent of attitude. The aerodynamic force will act only in the direction of the relative air velocity, 𝐯𝑟𝑒𝑙, and the solar force will only act along the sun vector. The tangential force components will cancel out.

The aerodynamic surface force on the sphere can be found by integrating equation (3-10) over half of the sphere surface (the other half will be shaded by the exposed half). The resulting force is:

𝐅𝑎𝑒𝑟𝑜,𝑠𝑝ℎ𝑒𝑟𝑒 = 𝜋𝜌|𝐯𝑟𝑒𝑙|2𝑅2[1 + 𝜎𝑡 2 + 𝜎𝑛( 2 3𝑟 − 1 2)] 𝐯̂𝑟𝑒𝑙 10-5

Where 𝜎_𝑛 and 𝜎_𝑛 are the surface accommodation coefficients as before, 𝑟 = 𝑣𝑏

|𝐯_𝑟𝑒𝑙| is the ratio of exit molecule velocity to mean incoming particle velocity, and R is the radius of the sphere. By equating the

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above force to the simplified drag equation (3-1) it is possible to find the equivalent drag coefficient for a sphere. With the surface parameters in Table 3-1, this yields a drag coefficient of 2.05.

The solar force is obtained by similar means. Integrating equation (3-12) over half the sphere results in the following expression for the solar force (Wertz, 1978)

𝐅𝑠𝑜𝑙𝑎𝑟,𝑠𝑝ℎ𝑒𝑟𝑒 = 𝜋𝑃𝑅2[ 1 + 𝜌𝑠 2 + 4𝜌𝑑 9 ] 𝐬 10-6

In equation (10-6) the fraction of transmitted photons was omitted to simplify the equation. It can thus not be applied to transparent membrane material. For a transparent membrane the integration should be extended to cover the inner surface of the sphere.

Mass Requirement

The relationship between the sub-system mass and balloon area is given by the following equation

𝑚𝑠𝑝ℎ𝑒𝑟𝑒 = 4𝜋𝑅2𝜌𝑒𝑛𝑣𝑒𝑙𝑜𝑝𝑒+ 𝑚𝑖𝑛𝑓𝑙𝑎𝑡𝑖𝑜𝑛 10-7

Where 𝑚_{𝑠𝑝ℎ𝑒𝑟𝑒} is the mass of the balloon sub-system, R is the radius, 𝜌_{𝑒𝑛𝑣𝑒𝑙𝑜𝑝𝑒} is the areal density of the envelope material and 𝑚𝑖𝑛𝑓𝑙𝑎𝑡𝑖𝑜𝑛 is the combined mass of the inflation gas and inflation system.

The typical values for the envelope material density and inflation system mass can be found from the Echo balloon specifications (Staugaitis & Kobren, 1966). Echo 1 and 1A used 12.5 µm thick Mylar with areal density of 17.5g/m2_{. It is anticipated that newer inflatable structures will attempt to make use of}

thinner material and 7 µm Mylar is assumed for the inflation-maintained envelope material. The mass of the canister carrying the inflation chemicals and the mass of the chemicals themselves totalled 32 kg. The rigidisable membrane of Echo II used a Mylar-Aluminium laminate. An areal density of 45 g/m2 _is

assumed for the 4.5 µm Al - 9 µm Mylar – 4.5 µm Al membrane including adhesives. It is further assumed that the same inflation system mass as before will suffice.

Table 10-1 Mass properties for an inflatable sphere deorbiting system

𝝆𝒆𝒏𝒗𝒆𝒍𝒐𝒑𝒆 (g/m2) 𝒎𝒊𝒏𝒇𝒍𝒂𝒕𝒊𝒐𝒏 (kg)

Rigidisable envelope 45.0 32

Inflation-maintained envelope 10.4 32

It is recognised that the inflation system mass mentioned above is appropriate for large diameter spheres. Smaller balloons can likely be inflated with lighter inflation system mass.

Collision energy and fragmentation risk

The collision energy-to-target-mass ratio (EMR) can be calculated in a similar fashion to the findings for the sail and host satellite in Table 3-3. For both the rigidisable and inflation maintained envelope, impacts with the membrane from a range of objects has EMR below the 10 J/g threshold. It is thus only impacts with the host satellite body that lead to fragmentation.

Operation, Integration and sub-system requirements

An inflatable sphere poses the same advantage as a drag-sail in that it can be used for a passive deorbiting strategy. But it also suffers from the same restriction in that it will only allow for an uncontrolled re-entry.

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The use of such a system is thus limited to situations where the host satellite will completely disintegrate when entering the atmosphere or where the fragments that do survive have a low enough casualty risk. The operational constraints for the inflatable sphere are very much the same as with a drag sail. It is also anticipated that after deploying the structure there will be no intervention from ground and the host satellite does not have to remain functional. In the case of an inflation-maintained envelope the inflation system might impose constraints on the host satellite, since it will have to maintain the pressure inside the sphere. If such functionality depends on active sub-systems it may count against this deorbiting alternative.